Both groups are Carmelites, but the “lay Carmelites” ordinarily refers to the laity within the Calced Carmelites. The “secular Carmelites” are the laity within the Discalced Carmelites. You easily can tell which order of Carmelites a particular group belongs to by looking at its shield. The Discalced Carmelites’ shield will have a cross in the center.
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